Assuming a series of independent events, probability of the event occurring on a given day is a poisson distribution with λ=0.8. This includes probability of event occuring 0, 1, 2, 3... times.
Considering only the days where the number of events is > 0 (using λ=0.8, probability of this occurring is):
$$\sum\limits_{y=1}^\infty \frac{\lambda^ye^{-\lambda}}{y!}=0.55067$$
I'm trying to work out what the average number of events would be ONLY considering the days where the number of events > 0 (ie 1, 2, 3...).